Let St be the value corresponding to some parameter t. For i j k and given values. Si the interpolated value at j by Inter[j, (i, s), (k, sk)]. Let 0 a y M. and Sk denote Suppose so and SM are known. We can estimate the value of sa as a = Inter[a, (0, so), (M, SM)], the value of sp as b = Inter [, (0, so), (M, SM)] and the value of sy as c = Inter[y, (0, so), (M, SM)]. Now if we consider the value of Sa and sy are known and are equal to the values of a and c respectively as computed above, we can also compute a possibly different estimate for sp as b* = Inter [, (a, a), (y, c)]. Let k>0 be a constant. Let r be the volatility for term T. We regard t to be st in the inquiry above with the interpolation method where we set = i. k k =(7-To) or + (-7) r for To TT T-To- T-To- When k = 1, do you think b=b* always? If yes, please prove it mathematically; if no please provide a counterexample ii. == When k 2, do you think b=b* always? If yes, please prove it mathematically; if no please provide a counterexample Your answer: